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A new collocation method for solution of mixed linear Integro-differential difference equations

Year 2015, Volume: 3 Issue: 2, 133 - 146, 19.01.2015

Abstract

The aim of this article is to present an efficient numerical procedure for solving mixed linear integro-differential-differenceequations. Our method depends mainly on a Taylor expansion approach. This method transforms mixed linear integro-differentialdifference equations and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. Thereliability and effiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computerprogram in Maple10

References

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  • M. G¨ulsu, M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007) 446-4
  • M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol. 25 (5) (1994) 625-633.
  • M. Sezer, M. G¨ulsu, A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument, Appl. Math. Comput. 171 (2005) 332-344.
  • S. Yalc¸ınbas¸, M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000) 291-308.
  • M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
  • S¸. Nas, S. Yalc¸ınbas¸, M. Sezer, A method for approximate solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
  • A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79 (9) (2002) 987-1000.
  • M. G¨ulsu, M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math 82 (5) (2005) 629-642.
  • B. B¨ulb¨ul, M. G¨ulsu, M. Sezer, A new Taylor collocation method for nonlinear Fredholm-Volterra integro-differential equations, Numer. Methods Partial Diff. Eq. doi 10.1002/num.20470.
  • T. L. Saaty Modern Nonlinear Equations, Dover Publications Inc., New York, 1981.
  • F. Karakoc¸, H. Bereketo˘glu, Solutions of delay differential equations by using differential Transform method, Int. J. Comput. Math. 86 (2009) 914-923.
  • M. Sezer, S. Yalc¸ınbas¸, N. S¸ahin, Approximate solution of multi-pantograph equation with variable coefficients, J. Comput. Appl. Math. 214 (2008) 406-416.
  • B. G¨urb¨uz, M. G¨ulsu, M. Sezer, Numerical approach of high-order linear delay difference equations with variable coefficients in terms of Laguerre polynomials, Math. Comput. Appl., 16 (2011) 267-278.
  • B. G¨urb¨uz, M. Sezer, Laguerre collocation method for solving Fredholm integro-differential equations with functional arguments, J. Appl. Math. 2014 (2014) 12.
Year 2015, Volume: 3 Issue: 2, 133 - 146, 19.01.2015

Abstract

References

  • S. Yalc¸ınbas¸, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput. 127 (2002)196- 20
  • M. G¨ulsu, M. Sezer, On the solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007) 446-4
  • M. Sezer, Taylor polynomial solution of Volterra integral equations, Int. J. Math. Educ. Sci. Technol. 25 (5) (1994) 625-633.
  • M. Sezer, M. G¨ulsu, A new polynomial approach for solving difference and Fredholm integro-difference equations with mixed argument, Appl. Math. Comput. 171 (2005) 332-344.
  • S. Yalc¸ınbas¸, M. Sezer, The approximate solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor polynomials, Appl. Math. Comput. 112 (2000) 291-308.
  • M. Sezer, A method for approximate solution of the second order linear differential equations in terms of Taylor polynomials, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
  • S¸. Nas, S. Yalc¸ınbas¸, M. Sezer, A method for approximate solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Educ. Sci. Technol. 27 (6) (1996) 821-834.
  • A. Karamete, M. Sezer, A Taylor collocation method for the solution of linear integro-differential equations, Int. J. Comput. Math. 79 (9) (2002) 987-1000.
  • M. G¨ulsu, M. Sezer, A method for the approximate solution of the high-order linear difference equations in terms of Taylor polynomials, Int. J. Comput. Math 82 (5) (2005) 629-642.
  • B. B¨ulb¨ul, M. G¨ulsu, M. Sezer, A new Taylor collocation method for nonlinear Fredholm-Volterra integro-differential equations, Numer. Methods Partial Diff. Eq. doi 10.1002/num.20470.
  • T. L. Saaty Modern Nonlinear Equations, Dover Publications Inc., New York, 1981.
  • F. Karakoc¸, H. Bereketo˘glu, Solutions of delay differential equations by using differential Transform method, Int. J. Comput. Math. 86 (2009) 914-923.
  • M. Sezer, S. Yalc¸ınbas¸, N. S¸ahin, Approximate solution of multi-pantograph equation with variable coefficients, J. Comput. Appl. Math. 214 (2008) 406-416.
  • B. G¨urb¨uz, M. G¨ulsu, M. Sezer, Numerical approach of high-order linear delay difference equations with variable coefficients in terms of Laguerre polynomials, Math. Comput. Appl., 16 (2011) 267-278.
  • B. G¨urb¨uz, M. Sezer, Laguerre collocation method for solving Fredholm integro-differential equations with functional arguments, J. Appl. Math. 2014 (2014) 12.
There are 15 citations in total.

Details

Journal Section Articles
Authors

Burcu Gürbüz This is me

Berna Bülbül Aslan This is me

Mehmet Sezer This is me

Publication Date January 19, 2015
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Gürbüz, B., Aslan, B. B., & Sezer, M. (2015). A new collocation method for solution of mixed linear Integro-differential difference equations. New Trends in Mathematical Sciences, 3(2), 133-146.
AMA Gürbüz B, Aslan BB, Sezer M. A new collocation method for solution of mixed linear Integro-differential difference equations. New Trends in Mathematical Sciences. January 2015;3(2):133-146.
Chicago Gürbüz, Burcu, Berna Bülbül Aslan, and Mehmet Sezer. “A New Collocation Method for Solution of Mixed Linear Integro-Differential Difference Equations”. New Trends in Mathematical Sciences 3, no. 2 (January 2015): 133-46.
EndNote Gürbüz B, Aslan BB, Sezer M (January 1, 2015) A new collocation method for solution of mixed linear Integro-differential difference equations. New Trends in Mathematical Sciences 3 2 133–146.
IEEE B. Gürbüz, B. B. Aslan, and M. Sezer, “A new collocation method for solution of mixed linear Integro-differential difference equations”, New Trends in Mathematical Sciences, vol. 3, no. 2, pp. 133–146, 2015.
ISNAD Gürbüz, Burcu et al. “A New Collocation Method for Solution of Mixed Linear Integro-Differential Difference Equations”. New Trends in Mathematical Sciences 3/2 (January 2015), 133-146.
JAMA Gürbüz B, Aslan BB, Sezer M. A new collocation method for solution of mixed linear Integro-differential difference equations. New Trends in Mathematical Sciences. 2015;3:133–146.
MLA Gürbüz, Burcu et al. “A New Collocation Method for Solution of Mixed Linear Integro-Differential Difference Equations”. New Trends in Mathematical Sciences, vol. 3, no. 2, 2015, pp. 133-46.
Vancouver Gürbüz B, Aslan BB, Sezer M. A new collocation method for solution of mixed linear Integro-differential difference equations. New Trends in Mathematical Sciences. 2015;3(2):133-46.